On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.

The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations

In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems. © 2012 American Institute of Physics.

Das transformadas integrais ao cálculo fracionário aplicado à equação logística

Pós-graduação em Biometria - IBB

Fractal concepts in relation to soil water diffusivity

Fractal geometry would appear to offer promise for new insight on water transport in unsaturated soils, This study was conducted to evaluate possible fractal influence on soil water diffusivity, and/or the relationships from which it arises, for several different soils, Fractal manifestations, consisting of a time-dependent diffusion coefficient and anomalous diffusion arising out of fractional Brownian motion, along with the notion of space-filling curves were gleaned from the literature, It was found necessary to replace the classical Boltzmann variable and its time t(1/2) factor with the basic fractal power function and its t(n) factor, For distinctly unsaturated soil water content theta, exponent n was found to be less than 1/2, but it approached 1/2 as theta approached its sated value, This function n = n(theta), in giving rise to a time-dependent, anomalous soil water diffusivity D, was identified with the Hurst exponent H of fractal geometry, Also, n approaching 1/2 at high water content is a behavior that makes it possible to associate factal space filling with soil that approaches water saturation, Finally, based on the fractally interpreted n = n(theta), the coalescence of both D and 8 data is greatly improved when compared with the coalescence provided by the classical Boltzmann variable.

Cálculo fracionário aplicado ao movimento browniano

This work aims to study several diffusive regimes, especially Brownian motion. We deal with problems involving anomalous diffusion using the method of fractional derivatives and fractional integrals. We introduce concepts of fractional calculus and apply it to the generalized Langevin equation. Through the fractional Laplace transform we calculate the values of diffusion coefficients for two super diffusive cases, verifying the validity of the method

Ordinary fractional differential equations are in fact usual entire ordinary differential equations on time scales

Despite the huge number of works considering fractional derivatives or derivatives on time scales some basic facts remain to be evaluated. Here we will be showing that the fractional derivative of monomials is in fact an entire derivative considered on an appropriate time scale.

A prelude to the fractional calculus applied to tumor dynamic

In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i.e., we replace the ordinary derivative of order 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 1, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.

Toward the Optimization of an e-Tongue System Using Information Visualization: A Case Study with Perylene Tetracarboxylic Derivative Films in the Sensing Units

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stability of multistep second derivative methods for integro-differential equations

The stability of multistep second derivative methods for integro-differential equations is examined through a test equation which allows for the construction of the associated characteristic polynomial and its region of stability (roots in the unit circle) at a proper parameter space. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A duplicated nitrotienyl derivative with antimycobacterial activity: synthesis, X-ray crystallography, biological and mutagenic activity tests

A duplicated nitrotienyl derivative was obtained as a by-product from the synthesis of a proposed molecular hybrid of a nitrotienyl derivative and isoniazid with an expected dual antimycobacteria mechanism. The structure was shown to be the 5,5'-dinitro-2(2,3-diaza-4-(2'-tienyl)buta-1,3-dienyl)tiophene by X-ray crystallography. The minimal inhibitory concentration (MIC) determination of this compound proved to be promising against Mycobacterium pathogenic strains such as M. avium and M. kansasei, although it had a high level of mutagenicity, as observed in mutagenic activity tests. (c) 2006 Elsevier Masson SAS. All rights reserved.

Synthesis, ex Vivo and in Vitro Hydrolysis Study of an Indoline Derivative Designed as an Anti-Inflammatory with Reduced Gastric Ulceration Properties

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Development and Validation of an UV-Derivative Spectrophotometric Method for Determination of Glimepiride in Tablets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comparative study of analytical methods by direct and first-derivative UV spectrophotometry for evaluation of losartan potassium in capsules

O losartano potássico é um agente anti-hipertensivo não peptídico, que exerce sua ação por bloqueio específico dos receptores da angiotensina II. Este trabalho propôs a validação e aplicação de métodos analíticos orientados ao controle de qualidade de losartano potássico 50 mg na forma farmacêutica cápsula, utilizando a espectrofotometria direta e derivada de primeira ordem na região do UV. Baseado nas características espectrofotométricas de losartano potássico, um sinal a 205 nm do espectro de ordem zero e um sinal a 234 nm do espectro de primeira derivada foram adequados para a quantificação. Os resultados foram usados para comparar essas duas técnicas instrumentais. O coeficiente de correlação entre as respostas e as concentrações de losartano potássico na faixa de 3,0-7,0 mg L-1 e 6,0-14,0 mg L-1 para espectrofotometria direta e derivada de primeira ordem em solução aquosa, respectivamente, foi de (r) of 0,9999 para ambos os casos. Os métodos foram aplicados para quantificação de losartano potássico em cápsulas obtidas de farmácias de manipulação locais e demonstraram ser eficientes, fáceis de aplicar e de baixo custo. Além disso, não necessitam de reagentes poluentes e requerem equipamentos economicamente viáveis.

Performance characteristics of high performance liquid chromatography, first order derivative UV spectrophotometry and bioassay for fluconazole determination in capsules

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)